Geometric Computing with Clifford Algebras: Theoretical Foundations and Applications in Computer Vision and Robotics

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Gerald Sommer
Springer Science & Business Media, May 22, 2001 - Computers - 551 pages
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Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work outlines that Clifford algebra provides a universal and powerfull algebraic framework for an elegant and coherent representation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism.
  

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Contents

New Algebraic Tools for Classical Geometry
3
Generalized Homogeneous Coordinates
27
Spherical Conformal Geometry with Geometric Algebra
61
A Universal Model for Conformal Geometries
77
GeoMAP Unification
105
Honing Geometric Algebra for Its Use in the Computer
127
Algebraic Embedding of Signal Theory and Neural
153
E RundbladLabunets
155
Clifford Algebra Multilayer Perceptrons
315
Geometric Algebra for Computer Vision and Robotics
335
3DReconstruction from Vanishing Points
371
Analysis and Computation of the Intrinsic Camera
393
CoordinateFree Projective Geometry for Computer
415
The Geometry and Algebra of Kinematics
455
Kinematics of Robot Manipulators
471
Using the Algebra of Dual Quaternions for Motion
489

Noncommutative Hypercomplex Fourier Transforms
187
Commutative Hypercomplex Fourier Transforms
209
Fast Algorithms of Hypercomplex Fourier Transforms
231
Local Hypercomplex Signal Representations
255
Introduction to Neural Computation in Clifford Algebra
291
The Motor Extended Kalman Filter for Dynamic Rigid
501
References
531
A Rockwood Y Zhang
532
Author Index
543
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